Another approach that uses sequential importance-sampling steps is sequential
Monte Carlo (SMC), also known as particle filtering
[1]}, [2]}, [3]}.
Recently, SMC algorithms have been developed for approximating the posterior
distribution of phylogenetic trees [4]}, [5]}, [6]}.
While inferring the posterior, SMC algorithms can approximate the marginal
likelihood of the model “for free,” by keeping a running average of the
importance-sampling weights of the trees (particles) along the way.
SMC algorithms hold a lot of promise for complementing MCMC in Bayesian
phylogenetics due to their sequential nature and ease with which the
computations can be parallelized
[4]}, [8]}, [9]}, [6]}.
See [5]} for an accessible treatment
of SMC in phylogenetics.
